Intrinsic approach to Galois theory of q-difference equations / Lucia Di Vizio, Charlotte Hardouin ; with a preface to Part 4 by Anne Granier.

Format:

Book

Author/Creator:

Di Vizio, Lucia, author.

Hardouin, Charlotte, 1977- author.

Contributor:

Granier, Anne, writer of preface.

Series:

Memoirs of the American Mathematical Society, 0065-9266 ; volume 279, number 1376

Language:

English

Subjects (All):

Galois theory.

Difference equations.

Physical Description:

xii, 70 pages ; 26 cm.

Place of Publication:

Providence : American Mathematical Society, 2023.

Summary:

"The Galois theory of difference equations has witnessed a major evolution in the last two decades. In the particular case of q-difference equations, authors have introduced several different Galois theories. In this memoir we consider an arithmetic approach to the Galois theory of q-difference equations and we use it to establish an arithmetical description of some of the Galois groups attached to q-difference systems"-- Provided by publisher.

Contents:

Generalities on q-difference modules

Formal classification of singularities

Rationality of solutions, when q is an algebraic number

Rationality of solutions when q is transcendental

A unified statement

The intrinsic Galois group

The parametrized intrinsic Galois group

Preface to Part 4 : The Galois D-groupoid of a q-difference system / by Anne Granier

Comparison of the parametrized intrinsic Galois group with the Galois D-groupoid.

Notes:

Includes bibliographical references.

ISBN:

9781470453848

1470453843

OCLC:

1358758417